WASHINGTON—The U.S. transferred 15 Guantanamo Bay detainees to the United Arab Emirates on Monday, the largest such movement yet in President Barack Obama’s push to remove most prisoners from the offshore prison before he leaves office in January.

The transfer of 12 Yemenis and three Afghans from the Cuba facility to the U.A.E. leaves 61 detainees, a significant drop from the 242 men imprisoned there in 2009 when Mr. Obama took office but short of the president’s longtime goal of closing the lockup.